The best answer we have to date is "Nobody knows," to which I would add, "nor do we know how to find out."
I see no shame in that answer. I'm surprised nobody suggested that answer so far, unless I missed it. That doesn't mean we'll never find out or make any progress, but we don't know now. Personally, I see value in such a direct answer.
If the question is "Are the laws of physics as we know them deterministic?" that's a question about human knowledge and the most effective equations and interpretations of them we have. We can answer that question definitively, but that doesn't answer the original question about the universe itself.
If the question is about the universe itself, all we can offer is the laws of physics we know, which brings us back to the first point.
We have incomplete knowledge of the universe. No experiment has been done yet to conclusively answer the question, so all we have is opinion. Anyone suggesting otherwise either knows of an experiment I don't (I'd be overjoyed to find out), or stating mere opinion. Opinion is nice, but it answers the question "Do you think the universe is deterministic," which is not the question asked.
Edit: I see someone put this answer on the original site.
When discussing the double-slit experiment, he said:
"It is not a lack of unknown gears - a lack of internal complications - that makes nature have probability in it; it seems to be in some sense intrinsic.
Someone has said it this way: 'nature herself doesn't know which way the electron is going to go.' A philosopher once said (a pompous one): 'it is necessary for the very existence of science that the same conditions always produce the same result.' Well, they don't: if you set up electrons in any way - I mean, you set up the circumstance here, in the same conditions every time, and you cannot predict behind which hole you'll see the electron.
They don't - and yet the science goes on in spite of him."
Watch the full lecture here:
I posted a transcribed portion previously:
Have you heard about the EPR paradox ? Einstein, Podolsky, and Rosen believed there may have been "hidden variables" in the language of quantum mechanics which were not yet accounted for. These hidden variables, if discovered, would render quantum mechanics more deterministic.
This idea was essentially shattered by Bell's theorem . The universe probably is not deterministic (at least in the sense we think about determinism). That's a hard pill to swallow, and it goes against all human intuition. But the majority of physicists do seem to accept this fact, however uncomfortable it might initially feel.
It really doesn't contradict "all human intuition". Strong determinism has always been a controversial position, though its popular with the people that view science as a new complete-and-all-encompassing religion rather than a utilitarian tool.
I realize what you're grasping at is that deterministic behavior might somehow underly this seemingly nondeterministic behavior. Bell's theorem, however, has made it difficult to reject that the this fundamental aspect of the universe is hard to explain without assuming nondeterminism (or superdeterminism).
I agree you can't prove it. You just haven't really explained why you're leaning toward the deterministic side.
While our scientific models are clearly in some sense about The World, they are still just models, and as dependent on the properties of our own minds as they are on the World. Some sort of direct-knowledge of The World is a nebulous concept.
I think many people have made this point, but it is perhaps most associated with the philosophy Immanuel Kant, who made the distinction between noumena, or 'the-world-in-itself', and phenomena, 'the-world-for-us'.
Well, it's stack exchange. You can't answer in a way that implies you don't know. They force answerers to act like everything is known, and that they personally know everything. Example: http://gamedev.stackexchange.com/questions/65768/how-can-i-d...
The idea is: suppose there is a universe that has elements that are fundamentally random. It is nondeterministic. Well, let that universe run for its lifetime, and record everything that happens. Then make a deterministic universe that just plays back the recording (this is the "second time around").
From the viewpoint of someone living inside the universe, there is no way to tell whether it is the first time around or the second time around.
But the other thing to point out is that this question presumes an old idea about the passage of time, which is that things happen in a sequence A, B, C, D, ... and that if you are at C then D "has not happened yet". But if you look at relativity, this appears to be a naïve viewpoint. In relativity, the time at a faraway point in space that you would consider "simultaneous" with your own clock depends on the relative speed between you and that point. As you speed up and slow down, you can make a faraway point "go forward or backward in time" with regard to which moment there you would consider "now". The crazy thing is that for angular movements the relative speed is amplified by distance, so when you are moving around at everyday speeds the "now" on planets across the galaxy is going back and forth by thousands or millions of years. (This is hard to observe because you are viewing tiny amounts of light from very very far away that have been traveling for a very long time, and the light that you are about to see was very close to you when you did the angular movement so it will not be much affected, etc, but hey, the math says what it says, you either believe what physics tells you or you don't.)
So when you make a distant "now" go forward, then backward, then forward again, do you expect the two forwards to be the same, or not?
This argument is not interesting, because "there is no way to know" is a correct but useless answer for basically any physical question.
The best thing we know how to do is to look at the evidence that nature gives us, and try to construct a description of nature from them. We will have different confidence levels for different descriptions (e.g. deterministic vs. non-deterministic), based on how well they match the evidence, but we can never know for sure. Therefore the interesting question is how confident are we that nature is deterministic / non-deterministic.
> But the other thing to point out is that this question presumes an old idea about the passage of time, which is that things happen in a sequence A, B, C, D, ... and that if you are at C then D "has not happened yet". But if you look at relativity, this appears to be a naïve viewpoint.
In relativity, the notion you described is replaced by the weaker notion of causality. It says that for each observer things will still happen in a well-defined sequence, even though different observers will not agree on questions such as "did these two events occur simultaneously?". The way these statements can be consistent, is that events for which there is no agreement on ordering can never influence each other (this is a mathematical result).
Due to causality, the question of whether nature is deterministic is well-defined even when relativity is taken into account.
Your second point is:
Again, this is true but irrelevant to the question at hand, due to causality.
I claim that both points are irrelevant. How is that agreeing with you?
1) If we define "universe" as "everything that exists" then you cannot record everything that happens. Because the record would be part of the universe and would have to recorded and the record of the record would have to be recorded...
2) The "first" and "second" universes would not be universes on their own. The "second" is a continuation of what you call the "first". So the system you describe would be random. Because the "deterministic" things that happen later on are based on the random things that happened earlier.
If you think of a universe as "everything I could see/touch/etc given infinite time", someone outside the universe who was in control of it might record it with no problem because they are not subject to the constraints of the universe. e.g. imagine the universe as being like a computer simulation that you programmed. You can probably pause it in a debugger any time you want, look at whatever state variables you want, etc.
So in this case the definition cannot be "everything that exists" because you have to define "exists" in the case where different sets of things may have different levels of "reality".
So there is no point in saying something is "outside" our universe and something is "inside".
But I think this is a little bit beside the point, because as I mentioned in my first post, all of this is predicated on us adopting the naïve view of time in our own universe, which is maybe not the best idea, given that we have plenty of evidence otherwise.
(And anyway, if you believe that "everything that exists" can be infinite, then there is no sense in saying our universe is being produced by some kind of simulation controlled in one particular other place, because of course it is, but actually this is probably happening in an infinite number of different ways from different places such that there is not really point any more in claiming that this is happening at all; the situation becomes such that you could just draw a relation between situation X and situation Y and could state that one could be causal of the other from a certain point of view.)
Assume, for the purpose of human communication, that "universe" means "a collection of all matter and space that can ever be observed or interacted with by an observer within and part of that universe".
This feels right on the surface, but is it actually true?
A quine contains a complete record of itself. That's an extreme case to be sure, but it does seem to provide at least one counterexample . . . (of a system that contains itself, not necessarily a system that actually observes and records itself)
A recording of a system does not need to contain everything in order for that recording to by played back, as long as the replay system is deterministic -- you just need to record the random inputs. E.g. see the way they do it in video games [http://www.gamedev.net/topic/439336-replay-system/]
I'm not saying that it is possible, just it shouldn't be dismissed out of hand just because it feels like it should be impossible.
This feels like it is either entirely incorrect, or you're taking something that is correct and interpreting it in a very misleading way.
Your remark about angular movements makes me think that perhaps you don't consider the fact that, when measured from a very distant planet, any angular movements we make in our everyday life are extremely tiny?
The angular movement thing is this: Imagine you have a frame of reference on the tip of your nose. The X axis points straight away from your face, the Y axis is to your left, Z is up. Now start turning your head to the left. To a tiny observer living on the tip of your nose, the relative speed along the Y axis of a faraway planet has suddenly become very high. The further the planet, the faster the speed (this part is just grade-school geometry).
So if you don't believe the extreme crazy case, think of the standard example: you get into a space ship or something and zip around really fast. And you are thinking about things closer to you. The math says the same thing: as your light cone changes, the set of spacetime intervals, that have time distance 0 from you, changes as well. So from your relative position the "now" at these faraway points goes back and forth. This is basic, basic relativity.
Science is a game we play where we do experiments, build theories, do more experiments, and so on.
Any scientific answer to how the universe works has to start with the assumption that the nature of universe can be understood in the first place (otherwise we'll never get anywhere.)
Edit: This was in response to your comment prior to edit. Up to "..."
As another example: did I really write this comment? Perhaps there was another universe where this comment was written, but _this_ universe is just a second-time-around recording where playback was started right after alternate-me hit post.
Anyway: the determinism question folks are talking about is, does the current state of the universe dictate the next state? In your playback universe, the answer is no -- you could edit any "frame" arbitrarily without affecting the frames that follow.
Hence a better question is, "is the universe deterministic, and free of nonlocal effects and hidden state?"
No it doesn't. You are assuming the existence of a recording device, and worse excluding the recording device from your definition of universe.
> Then make a deterministic universe that just plays back the recording (this is the "second time around").
What does play back even mean in this context? When you play back a recording the events in it do not actually occur again. All you are doing is perusing a memory.
Your recoding doesn't even need to simulate the laws of physics - it simply places objects where they were - if you wanted to you could make any changes you like. So you could make the recording do anything. i.e. a recording is meaningless - it's not actually a universe. (By universe I mean something that follows a defined set of rules.)
> From the viewpoint of someone living inside the universe, there is no way to tell whether it is the first time around or the second time around.
In the the second time around they are not actually living in the universe.
> make a faraway point "go forward or backward in time"
No you can't. You can make it traverse time faster or slower, but you can not make it go forward and backward.
> The crazy thing is that for angular movements the relative speed is amplified by distance, so when you are moving around at everyday speeds the "now" on planets across the galaxy is going back and forth by thousands or millions of years.
That is simply not true. Angular movement has exactly zero effect on relativity - it's not true motion which requires a relative difference in energy (AKA speed).
I just want to make a mention for this point. Ahh but you see, for all we know, the universe could have simply followed 'a set of rules' up till the point we are living at and until a set future point in the 'timeline' (or something we perceive as the timeline). Then all of a sudden all the laws we know will break because the 'universe' entity decides to play another recording. Then all of knowledge of the 'universe' collapses. I think this is what the parent was talking about. You cannot predict nor even conclude that such scenario cannot happen.
(Yes, at the level of the macroscopic world we can make consistently accurate predictions, but physicists would say this is because we are operating at a scale where the statistical nature of quantum mechanics averages out, etc. Unless you are Carver Mead or one of the other wave guide kinds of guys who believe there actually is no randomness in QM and it is deterministic all the way down.)
I think you are misinterpreting something. If this were true, you would be able to observe a supernova and play it back in time by simply shifting your nose (or camera) around. Which is evidently not true.
Let's assume that an argument is made asserting that quantum mechanics are not probabilistic and are actually deterministic over the entire area of the universe. The reason we see QM as a probabilistic feature of the universe is because our "determinism reference frame" is incomplete.
For example, within in the room you are sitting in right now there is a determinism reference frame that indicates that when you press a key on your keyboard a letter will appear on your monitor - that reference frame is actually incomplete. Half way across the galaxy a star could explode, the "cosmic ray" from that star could interact with our atmosphere and ultimately flip a bit in your RAM - causing a kernel panic in the worst case scenario. Computers are only deterministic machines if the determinism reference frame does not include the entire universe. This means to assert that something in our reality is truly deterministic we need to have perfect information about the entirety of our reality (I specifically avoid the word "universe" in that statement).
The next piece of information that is important is that physicists believe that our universe may have been formed within a Higg's Field (which is why the hunt for a Higg's boson is such an interesting area of physics). This means that there is plausibly a volume or something (not necessarily a universe itself) within which our universe was formed. Conjecture: is this encompassing "metareality" the reason we have non-determinism in quantum mechanics? Is our universe simply a "room" within another reality? Keep in mind, I am avoiding multiverse, the Higg's Field doesn't necessarily have to be compatible with the multiverse theory and it's hard to make the analogy I am trying to make without it sounding like I am venturing into that territory.
The problem is that we can only observe our own universe, if our universe does exist within another reality (which the existence of the Higg's boson points toward) it means that our universe is ultimately non-deterministic. It would be impossible to determine if that metareality is deterministic because we cannot observe it.
Therefore, there is a good chance that the universe is not deterministic. It is impossible to tell if reality is deterministic.
Edit: and then there is this . Determinism is very likely a human concept that has absolutely no meaning in terms of reality, it's a convenient simplification just like Newtonian physics.
It seems to me that determinism is a feature of the observer too. For example, roll of dice is non-deterministic for a human being, even in perfectly deterministic universe. It's just too complicated to simulate, so it appears random, and we can pretty much declare it to be non-deterministic.
And pseudo-random generators, purely idealized systems, can generate non-determinism from determinism. You can also have systems that do the opposite - that are itself based on non-determinism, but are in the effect deterministic. Classical computers use non-deterministic movement of electrons (or better say, they don't rely on their determinism), but can still produce repeatable (deterministic) results.
So you can move away from determinism or non-determinism on lower level (like the level of elementary particles) by various methods of aggregation. Considering there is still about 20 orders of magnitude between the "size" of elementary particles and Planck length, I would dare say that reality may still switch between determinism and non-determinism several times beyond the what we know.
Also, people may find this lecture by Dan Dennett interesting (which inspired the above argument): http://www.youtube.com/watch?v=uxup7sxIUmg
It's kind of (very) important for information theory and computability theory. If the universe is deterministic, a sufficiently small physical system can be exactly simulated by a sufficiently powerful Turing machine.
In simulations of physical systems, there already is a barrier of what we can do (chaotic behavior) regardless whether or not the underlying physics is deterministic or not. In other words, even if the question ("is universe deterministic") remains unanswered, we can already simulate all we need to the way it's possible to do it.
(BBC Radio 4 - In Our Time) - no idea if this is blocked outside the UK?
Gödel's amusing exercise is just a formalization of St. Anselm's, and most of the centuries of criticism of the latter can be applied to the former. In particular, his little proof has three definitions and six special-purpose axioms, and, in addition to all this, depends on a property of goodness or perfection that is only defined implicitly. Naturally, the existence of something that he interprets as "god" falls out as a theorem. Big deal.
The nature of mathematics are that the theorems are contained within the axioms. If the axioms are self-evident, and the conclusions are surprising, we have some interesting math. But at least two of Gödel's axioms are not self-evident. Therefore, this "proof" strikes me as a setup, and is not very interesting.
If you claim that goodness is artificial/relative/subjective, then you are hilariously self-refuting yourself. :)
Thus when saying morality is relative it's not that we say that the factuality of "X is moral" depends on your setting, but that the statement makes no sense unless you specify what morality you mean, because "moral" just means "acceptable in a given morality system".
Thanks for the kind mature words.
You are no different from the Christian fundamentalists who accuse that the scientists (including logicians like me) don't know what they are talking about. Sigh.
I was being respectful, but you showed your deficiency by attacking my intellect. Thanks for that.
I can only point in the right direction. I cannot rectify a highly deficient education (ah, the US).
I don't have the time to produce a formal proof right now, but ideas for directions:
1. It's a 'good' property to stop any 'bad' properties from existing (otherwise they're not really 'bad'). A godlike thing exists, and contains all good properties, thus nothing with 'bad' properties can exist. This is either a contradiction with reality if you take reasonable definitions for 'good' and 'bad', or proof that the 'good' and 'bad' in the proof are meaningless, should be replaced by 'X' and 'Y', and then neither of other assumptions is valid (could be X(essential) as well as Y(essential))
2. A property that is very good might force a property that is slightly bad on its own, and still be good in total. I'd guess this can't be formalized, since good and bad are so fuzzy in the entire proof.
Read the literature. Godel and many others have provided volumes supporting it.
You wouldn't walk into a physics department and claim that "black holes" are ridiculous right? Your nonchalant dismissal of the assumptions is sort of like a creationist claiming evolution is false because monkeys exist.
1. You have totally misunderstood the proof.
2. Homework: ponder why relativism is self-contradictory :).
The problem here is that we're all human and thus certain things are probably unknowable. You have disdain for someone who makes something up to fill that void, but I have disdain for someone who creates axioms in order to affirm their faith in science as the arbiter of truth. I am agnostic in the viewpoint that philosophy has a lot more to say on the subject than the either the worshiper of religious gods or the worshiper of science.
For me, I consider snarky smugness to be evidence of free will.
If we can agree that if a two systems are in the exact same state then they will continue to be in the same state in future, then we can say deduce that the universe is deterministic.
If a player hits a snooker ball exactly the same way two times, and all other balls are in the same position, the temperature is the same, humidity is the same, rotation of the earth is the same, rotation of electrons and unknown state of quarks are the same -- everything is the same -- then the result will be the same. To have a different outcome from the same inputs in a closed system is not possible.
The same goes for human thought. If your brain is in the same state twice, all neuro chemicals are in the same state and all external forces are the same, and you are posed with a problem twice, you will make the same decision twice. There is no other possible outcome, for if there were another outcome it would be due to a differing influence. Thus your decisions are effectually predetermined.
This the universe in its current state can only move forward in one way -- effectually predetermined.
If anyone can come up with a case that two closed systems that are in the same state can diverge, I'd love to hear it.
Specifically, I introduce the idea of a Stern-Gerlach experiment to measure the spin of an electron along specific directions. If you prepare an electron in (say) a "+z" state (which is absolutely unique and unambiguous) and then measure its spin along the perpendicular x-axis, the results are 50/50 (and completely unpredictable).
At this point, your intuition is crying out, "We must have just overlooked some distinguishing detail in that initial +z state!" But it turns out that there are experimentally testable predictions of that sort of "hidden information" theory that differ from the predictions of quantum theory (look up "Bell inequalities"), and experiments always come back saying that the quantum description is correct.
The fact that the x-axis spin results are 50/50 strongly suggests something very specific and deterministic is going on. It would seem that we just aren't able to (pre)determine it without influencing it.
I agree that this flies in the face of everything that seems sensible in the world. I loathed quantum mechanics for years for reasons along these lines. Nevertheless, the universe is under no obligation to obey my intuition for what is sensible, nor my sense of elegance and beauty. Much to my disappointment, experiments make it absolutely clear that we do not live in a universe where "common sense" arguments are at all trustworthy on the scale of individual particles.
(Also, personally, I would say that the 50/50 result on the x-axis is purely a consequence of symmetry: nothing in the initial state or the measurement apparatus is set up to prefer +x over -x or vice versa, so it would be more or less impossible for it to split any way other than 50/50.)
If you believe in the Copenhagen interpretation (and similar interpretations) then the universe isn't deterministic - there are many events that can happen but only one does happen in the end (when the set of probabilities assume specific values - the wavefunction collapse).
If you subscribe to the Many-worlds Interpretation then the universe is deterministic in a way - all events that could happen will happen in some branches (or in a portion of the branches equal to the probability of the event happening, as much as this makes sense) and it was all going to be that way since 'the beginning of time'. However, from another point of view (ours) - it isn't determined which branch you will experience yourself observing and this can make things seem non-deterministic (but in reality you or equivalents of you will experience yourself observing all branches in which you exist so I don't think that this would be the correct way to think about it).
The explanation of it I like best is this one (I don't remember where I originally read it):
It involves a two player game, the players completely separated from each other. Each is independently shown X or Y. Each player must then give either answer A and B. They win the game if:
- when both are shown X, they choose different answers
- otherwise, they choose the same answer
They can choose a strategy to follow before, but after they're physically separated, each player's decision can only depend on what they're shown (X or Y). Given this restriction, even allowing the players to have (pseudo-)non-deterministic strategies, they'll win with a chance of 75%.
However, if the players' strategy involves each having half of an entangled pair of photons, they can make measurements of its spin at one of two predetermined angles (P1X = 0, P2X = 67.5, P1Y = 45, P2Y = 22.5), based on if they see X or Y. Their answer is based on whether they get a spin-up or spin-down measurement. With this strategy, they win about 85% (cos^2(tau/16)) of the time.
Basically, a foremost expert on deterministic cellular automata is of the opinion that Universe is likely a cellular automaton, but not a deterministic one.
Which I find intriguing.
"Not only does God play dice, the dice are loaded"
BTW, related questions: is the universe finite? Is the universe discrete or continuous (or better, do you need infinite information to represent it)?
Not being able to record the state doesn't mean it isn't deterministic.
Within that framework, the most natural interpretation of this question might be, "Would it be possible in principle for a conscious being with perfect knowledge of the current state of the universe to predict the outcome that they would observe for any possible experiment?" Quantum mechanics answers this with an definitive "No." Even very simple systems can be prepared in a "superposition" of two possible states, in a sense that represents not just our ignorance of some underlying truth but a true mixture with measurable consequences.
On the other hand, you might intend the question to mean "Given complete knowledge of the current state of the universe, would it in principle be possible to predict the future state of the universe?" If we leave aside issues of "observers" and "collapse of the wave function" for the moment, quantum mechanics clearly says that the answer is "Yes". (The mathematical property involved is "unitarity of time evolution".) If you begin with an electron in a superposition of "spin up" and "spin down" states and make a measurement, then a few moments later your experimental apparatus will be in a specific corresponding superposition of "detected spin up" and "detected spin down" states.
But where you go from there depends on your preferred interpretation of quantum mechanics. The traditional Copenhagen interpretation says that once an observer looks at the measurement, the superposition state (the wave function) "collapses" to one answer or the other probabilistically, so determinism is lost. A "many-worlds" style interpretation would instead imply that the superposition of both outcomes persists in the state of the universe, but any particular instance of a given observer will see an outcome consistent with one measurement or the other (and the phenomenon of "decoherence" prevents those instances from interfering with each other in any meaningful way in the future).
[Edit to add a disclaimer: There are weird open questions related to quantum gravity and black holes that call the unitarity of quantum mechanics into some doubt: a study of effects like Hawking radiation that arise when studying quantum fields in curved space-time might suggest that information about the state of the universe is lost over time. My impression as someone working in this field is that most people expect deep down that unitarity will be preserved in an ultimate theory, but there's no way to be sure until we have one. Also, LQG folks may be less confident of how their model would ultimately answer that question than string theory folks like me tend to be.]
I think maybe you'd want to reference Heisenberg uncertainty here, not superposition? Superposition is weird, but deterministic except for the wave function collapse, but you correctly deal with that later. Its the Heisenberg uncertainty that prevents you from precisely measuring a particle's current state, thereby preventing you from obtaining fully predictive information except in philosophical hypotheticals.
So I stand by my "superposition" phrasing. :) Taking a measurement of a system that is in a superposition of distinct eigenstates of the observable being measured will give a probabilistic distribution of measurement outcomes (with probabilities derived from the amplitudes of the corresponding terms in the superposition).